The log-Sobolev inequality for spin systems of higher order interactions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909448067350528 |
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| author | Konstantopoulos, Takis Papageorgiou, Ioannis |
| author_facet | Konstantopoulos, Takis Papageorgiou, Ioannis |
| contents | We study the infinite-dimensional log-Sobolev inequality for spin systems on $\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that the one site measure without a boundary $e^{-ϕ(x)}dx/Z$ satisfies a log-Sobolev inequality and we determine conditions so that the infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete application, we prove that a certain class of nontrivial Gibbs measures with non-quadratic interaction potentials on an infinite product of Heisenberg groups satisfy the log-Sobolev inequality. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1906_11980 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The log-Sobolev inequality for spin systems of higher order interactions Konstantopoulos, Takis Papageorgiou, Ioannis Probability Mathematical Physics Functional Analysis 60K35, 26D10, 39B62, 22E30 We study the infinite-dimensional log-Sobolev inequality for spin systems on $\mathbb{Z}^d$ with interactions of power higher than quadratic. We assume that the one site measure without a boundary $e^{-ϕ(x)}dx/Z$ satisfies a log-Sobolev inequality and we determine conditions so that the infinite-dimensional Gibbs measure also satisfies the inequality. As a concrete application, we prove that a certain class of nontrivial Gibbs measures with non-quadratic interaction potentials on an infinite product of Heisenberg groups satisfy the log-Sobolev inequality. |
| title | The log-Sobolev inequality for spin systems of higher order interactions |
| topic | Probability Mathematical Physics Functional Analysis 60K35, 26D10, 39B62, 22E30 |
| url | https://arxiv.org/abs/1906.11980 |